Beyond Euclidean Geometry

To convert into binary, you have to consider how the number can be decomposed into a sum of power of 2. You must start from the highest power of two lower than your number.

So take your number 6 in your first problem. $$2^3 = 8$$ And so we must start at $$2^2$$ . We hence write 6 below:

$$6 = 1 \mbox{x} 2^2 + 1 \mbox{x} 2^1 + 0 \mbox{x} 2^0$$

You can read straight off this as 6 = 110 in binary

Oh well now that i look at what you are saying it seems very simply now, thank you!